What is the integral of 2cos(e^x)-2xe^xsin(e^x) ?

The integral of 2cos(e^x)-2xe^xsin(e^x) is 2xcos(e^x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 2cos(e^x)-2xe^xsin(e^x)

\int 2 cos (e^{x}) - 2 x e^{x} sin (e^{x}) d x

2 x cos (e^{x}) + C

Solution steps

\int 2 cos (e^{x}) - 2 x e^{x} sin (e^{x}) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 cos (e^{x}) d x - \int 2 x e^{x} sin (e^{x}) d x

\int 2 cos (e^{x}) d x = 2 Ci (e^{x})

\int 2 x e^{x} sin (e^{x}) d x = 2 (- x cos (e^{x}) + Ci (e^{x}))

= 2 Ci (e^{x}) - 2 (- x cos (e^{x}) + Ci (e^{x}))

Simplify

2 Ci (e^{x}) - 2 (- x cos (e^{x}) + Ci (e^{x})) : 2 x cos (e^{x})

= 2 x cos (e^{x})

Add a constant to the solution

= 2 x cos (e^{x}) + C

What is the integral of 2cos(e^x)-2xe^xsin(e^x) ?
The integral of 2cos(e^x)-2xe^xsin(e^x) is 2xcos(e^x)+C